Dot Product Calculator Quandry

I'm going nuts here and I can't figure this out. I have two complex vectors:A=(1+i)x + (1)y +(i)zB=(4-i)x +(0)y + (2-2i)z
If I do the dot product of these on my calculator I get 1 + 7i, however when I do this by hand I keep getting 7 +5i. What am I doing wrong? When figuring this out by hand I am going by the assumption that AB=AxBx + AyBy + AzBz.

Yes that's correct, for a complex inner product you take the conjugate of the second argument. It's defined that way so that if you take the inner product of a vector with itself then you'll always end up with just a real number. This real number is called the "norm" and is a generalized measure of the length of the vector.